Group Extensions, Gerbes and Twisted K-theory

Abstract: This thesis reviews the theory of group extensions, gerbes and twisted K-theory. Application to anomalies in gauge theory is briefly discussed. The main results are presented in two appended scientific papers. In the first paper we establish, by construction, a criterion for when an infinite dimensional abelian Lie algebra extension corresponds to a Lie group extension. In the second paper we introduce the fractional loop group L_qG, construct highest weight modules for the Lie algebra and discuss an application to twisted K-theory on G.